The dimensional formula for coefficient of self induction is

Options

A. `[ML^(2)T^(-2)A^(-2)]`
B. `[MLT^(-2)A^(-1)]`
C. `[ML^(2)T^(2)A^(-2)]`
D. `[ML^(2)T^(-2)A^(-1)]`

Explanation

To find the dimensional formula for the coefficient of self-inductance (L), we can start from the relationship between energy (U), self-inductance (L), and current (I). The formula we will use is:

\[ U = \frac{1}{2} L I^2 \]

### Step-by-step Solution:

1. **Rearranging the Formula**:
We can rearrange the formula to express L in terms of U and I:
\[ L = \frac{2U}{I^2} \]

2. **Identifying Dimensions**:
Next, we need to identify the dimensions of energy (U) and current (I):
- The dimensional formula for energy (U) is:
\[ [U] = M L^2 T^{-2} \]
- The dimensional formula for current (I) is:
\[ [I] = A \]

3. **Substituting Dimensions**:
Now, we substitute the dimensions of U and I into the formula for L:
\[ [L] = \frac{2[M L^2 T^{-2}]}{[I]^2} \]
Since \( [I] = A \), we have:
\[ [L] = \frac{M L^2 T^{-2}}{A^2} \]

4. **Final Expression**:
Thus, we can express the dimensional formula for self-inductance (L) as:
\[ [L] = M L^2 T^{-2} A^{-2} \]

### Conclusion:
The dimensional formula for the coefficient of self-inductance is:
\[ [M L^2 T^{-2} A^{-2}] \]